Jubilismic family

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The jubilismic family of rank-3 temperaments tempers out 50/49 in the full 7-limit. It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While many rank-3 temperaments are planar, a jubilismic temperament divides the octave in two. Related to this is the 2.5.7-subgroup {50/49} temperament jubilic.

Jubilismic

Subgroup: 2.3.5.7

Comma list: 50/49

Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]

mapping generators: ~7/5, ~3, ~5

Optimal tunings:

• WE: ~7/5 = 599.6673 ¢, ~3/2 = 702.5906 ¢, ~5/4 = 380.6287 ¢

error map: ⟨-0.665 -0.030 -7.016 +10.139]

• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.4574 ¢, ~5/4 = 380.0086 ¢

error map: ⟨0.000 +0.502 -6.305 +11.183]

Minimax tuning:

• 7- and 9-odd-limit

[[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]

unchanged-interval (eigenmonzo) basis: 2.3.35

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48, 60d

Badness (Sintel): 0.561

Scales: jubilismic10, jubilismic12

Jubilife

There is a natural extension of jubilismic to the 2.3.5.7.17 subgroup, which tempers out 85/84 and 120/119, and identifies 7/5 with 10/7, 17/12 and 24/17 as the semioctave.

Subgroup: 2.3.5.7.17

Comma list: 50/49, 85/84

Mapping: [⟨2 0 0 1 5], ⟨0 1 0 0 1], ⟨0 0 1 1 0]]

Optimal tunings:

• WE: ~7/5 = 599.8903 ¢, ~3/2 = 702.6008 ¢, ~5/4 = 379.6441 ¢
• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.5503 ¢, ~5/4 = 379.4777 ¢

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48

Badness (Sintel): 0.357

Undecimal jubilismic

Formerly known as jubilee, undecimal jubilismic tempers out 99/98 and 100/99, and is the most natural extension of jubilismic to the 11-limit. 11/8 is found by a stack of two 7/6's or two 5/3's octave reduced.

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98

Mapping: [⟨2 0 0 1 4], ⟨0 1 0 0 -2], ⟨0 0 1 1 2]]

Optimal tunings:

• WE: ~7/5 = 599.6219 ¢, ~3/2 = 702.9722 ¢, ~5/4 = 380.4574 ¢

error map: ⟨-0.756 +0.261 -7.369 +9.741 +0.628]

• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.9249 ¢, ~5/4 = 379.6796 ¢

error map: ⟨0.000 +0.970 -6.634 +10.854 +2.192]

Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48

Badness (Sintel): 0.673

Jubilee

Jubilismic temperament works on the no-13s 17-limit subgroup very well, where the semioctave stands in for ~7/5, ~17/12, ~99/70 and their octave complements.

Subgroup: 2.3.5.7.11.17

Comma list: 50/49, 85/84, 99/98

Mapping: [⟨2 0 0 1 4 5], ⟨0 1 0 0 -2 1], ⟨0 0 1 1 2 0]]

Optimal tunings:

• WE: ~7/5 = 599.8463 ¢, ~3/2 = 702.9469 ¢, ~5/4 = 379.5011 ¢
• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.9274 ¢, ~5/4 = 379.2350 ¢

Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48

Badness (Sintel): 0.578

Festival

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49

Mapping: [⟨2 0 0 1 -4], ⟨0 1 0 0 2], ⟨0 0 1 1 1]]

Optimal tunings:

• WE: ~7/5 = 600.8501 ¢, ~3/2 = 694.6084 ¢, ~5/4 = 371.7918 ¢

error map: ⟨+1.700 -5.646 -11.121 +7.216 +13.091]

• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 694.5001 ¢, ~5/4 = 372.9799 ¢

error map: ⟨0.000 -7.455 -13.334 +4.154 +10.662]

Optimal ET sequence: 10, 12, 22e, 26

Badness (Sintel): 0.827

Fiesta

Subgroup: 2.3.5.7.11

Comma list: 50/49, 56/55

Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]

Optimal tuning:

• WE: ~7/5 = 596.3068 ¢, ~3/2 = 709.1930 ¢, ~5/4 = 395.2472 ¢

error map: ⟨-7.386 -0.148 -5.839 +7.955 +22.830]

• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.6819 ¢, ~5/4 = 391.4911 ¢

error map: ⟨0.000 +7.727 +5.177 +22.665 +48.682]

Optimal ET sequence: 8d, 10, 12, 22e, 30dee, 42ddeee

Badness (Sintel): 0.861

Jamboree

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54

Mapping: [⟨2 0 0 1 2], ⟨0 1 0 0 3], ⟨0 0 1 1 -1]]

Optimal tunings:

• WE: ~7/5 = 600.0436 ¢, ~3/2 = 706.7073 ¢, ~5/4 = 376.8582 ¢

error map: ⟨+0.087 +4.839 -9.281 +8.250 -7.880]

• CWE: ~7/5 = 600.0000 ¢, ~3/2 = 706.7334 ¢, ~5/4 = 376.9332 ¢

error map: ⟨0.000 +4.778 -9.381 +8.107 -8.051]

Optimal ET sequence: 8d, 10, 12e, 14c, 22, 58ce

Badness (Sintel): 0.938